Discounted risky asset stochastic process problem

$S_t$ is the random variable representing the risky asset price at time $t$.

M_t is the riskless asset. They are governed by the equations

$\frac{dS_t}{dt}=\mu dt + \sigma dZ_t$ and

$dM_t = rM_t dt$

where $Z_t$ is Brownian motion. If we define the discounted risky asset by $S_t^{*}=S_t/M_t$. How does the process $S_t^{*}$ become governed by

$\frac{dS_t^{*}}{dt}=(\mu-r) dt + \sigma dZ_t$ ?

I cannot see why you subtract $rdt$.

• Do you mean S(t)udt in the GBM equation? – HelloWorld Aug 18 '14 at 4:30

$$\textbf{Preface}$$ I am assuming log normal asset but this is not clear from the question? Or rather I have misinterpreted the question!
Well as I see it from a a purely mathematical exercise $$d\left(\dfrac{S_t}{M_t}\right) =\frac{1}{M_t}dS_t - \frac{S_t}{M_t^2}dM_t +O(dt^2)$$
or finally $$\frac{dS^*_t}{S^*_t} = (\mu-r)dt+\sigma dZ_t$$